元素加权中智相关系数在RGBD视频跟踪中的应用
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"元素加权中智相关系数及其在改进RGBD视频中CAMShift跟踪器中的应用"
本文是一篇研究论文，主要探讨了中智相关系数（Neutrosophic Correlation Coefficient）的概念，并提出了一种新的元素加权中智相关系数。中智集（Neutrosophic Set，NS）是哲学的一个新分支，用于处理不确定性、模糊性和中性状态的问题。在模糊逻辑和不确定性理论领域，已经提出了多种相关系数和相似度衡量方法。然而，作者指出，在中智集的三个元素——真（Truth）、不确定（Indeterminacy）和假（False）中，可能存在不同的贡献程度。
在该研究中，作者引入了元素加权的概念，以更精确地反映这些元素对整体关联度的影响。通过这种方法，他们改进了中智集中的相关性计算，使得在处理复杂和不确定数据时能提供更准确的结果。这一创新对于处理现实世界中的不完整和不精确信息特别有用，例如在图像处理和目标跟踪等领域。
文章进一步将这种新的元素加权中智相关系数应用于改进RGBD（红绿蓝深度）视频中的CAMShift跟踪器。CAMShift是一种基于光流的自适应跟踪算法，它能够连续追踪目标在视频序列中的运动。然而，由于RGBD视频包含额外的深度信息，传统的CAMShift可能在处理这种数据时遇到挑战，特别是在存在噪声和遮挡的情况下。
通过集成新的相关系数，作者提出的改进版CAMShift跟踪器能够更好地处理RGBD视频中的不确定性，提高跟踪性能。这可能涉及到更准确地估计目标的运动、更好地适应光照变化以及在目标部分被遮挡时仍保持稳定跟踪。此外，该方法还可能提高在复杂背景和目标形状变化情况下的鲁棒性。
这篇论文为理解和应用中智集提供了一个新的视角，特别是在处理不确定性和模糊性的实际问题上。提出的元素加权中智相关系数不仅丰富了模糊系统理论，还为RGBD视频的跟踪算法带来了显著的改进，为未来的研究和应用开辟了新的方向。
Information 2018, 9, 126 4 of 16
where
α
,
β
,
γ ∈
[0,1],
α
+
β
+
γ
= 1. Then
S
e
(A
i
,
A
j
)
is actually the cosine value between the vector
(
√
αT
C
k
(A
i
)
,
p
βI
C
k
(A
i
)
,
√
γF
C
k
(A
i
))
and
(
√
αT
C
k
(A
j
)
,
p
βI
C
k
(A
j
)
,
√
γF
C
k
(A
j
))
. Hence, it is easy to
find that Se satisfies the following properties:
(SP1) 0 ≤ S
e
(A
i
, A
j
) ≤ 1;
(SP2) S
e
(A
i
, A
j
) = S
e
(A
j
, A
i
);
(SP3) S
e
(A
i
, A
j
) = 1 i f A
i
= A
j
;
Then the element-criterion-weighted correlation coefficient between A
i
and the ideal alternative
A* is defined as
WS
e
(A
i
, A
∗
) =
n
∑
k=1
w
k
αT
C
k
(A
i
)T
C
k
(A
∗
)+βI
C
k
(A
i
)I
C
k
(A
∗
)+γF
C
k
(A
i
)F
C
k
(A
∗
)
q
αT
C
k
2
(A
i
)+βI
C
k
2
(A
i
)+γF
C
k
2
(A
i
)
q
αT
C
k
2
(A
∗
)+βI
C
k
2
(A
∗
)+γF
C
k
2
(A
∗
)
(6)
3. Improved CAMShift Visual Tracker Based on the Neutrosophic Theory
The algorithmic details of the proposed tracker are presented in this section.
A rectangle bounding box [
22
,
23
] is always employed for the representation of the target location
when dealing with the visual tracking problem. For a visual tracker, the critical task is to estimate the
corresponding bounding box in each frame.
Algorithm 1 illustrates the basic flow of the proposed algorithm, as seen in Table 1. Details of
each main step are given in the following subsections.
Table 1. Basic flow of the NeutRGBDs tracker.
Algorithm 1 NeutRGBDs
Initialization
Input: 1st video frame in the RGBD domain
(1) Select an object on the image plane
(2) Extract object seeds using both color and depth information
(3) Extract object region using object seeds and the information of the depth segmentation
(4) Calculate the corresponding color and depth histograms as target model
Tracking
Input: (t+1)-th video frame in the RGBD domain
(1) Calculate back-projections in both color (P
c
) and depth domain (P
D
)
(2) Calculate fused back-projection (P) using neutrosophic theory
(3) Calculate the bounding box of the target in the CAMShift framework
(4) Extract object region and update object model and seeds
(5) Modify the scale of the bounding box in neutrosophic domain
Output: Tracking location
3.1. Selecting Object Seeds
Assuming the tracker can calculate an adequate bounding box, and
R
is the extracted object
region, then it is reasonable that we assume pixels located in
R
and the bounding box with smaller
depth value are more likely to be a part of the target.
To select robust object seeds, the pixels located in R and the bounding box are first sorted by the
descending order of the depth value. Then several pixels are selected as the candidate object seeds set
S
by sampling the sorted pixels with a fixed sampling space. Considering there may exists background
regions in the corresponding area, only the top 50 percent pixels in the sorted pixel set are sampled.
For the proposition of depth value is a critical criterion for judging the object seed, T
D
, I
D
, and F
D
represent the probabilities when a proposition is true, indeterminate and false degrees, respectively.
Then we can give the definitions:
T
D
=
r
max
−r
si
r
max
(7)
I
D
= var(D(ROI
si
)) (8)
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